How to identify and differentiate frequency and time in EEG data using python?

Question

I have an EEG data of 200 Hz and sampled at 4097. I have few doubts and questions related to this data:

1. What does it mean by sampling in EEG data?
2. I am getting the sample rate and the frequency when I plot the data as shown below. Shouldn't it be the time and frequency?

I don't understand what I'm missing here. Can anyone explain how am I supposed to identify the time and frequency of EEG data?

EEG data file : http://filesave.me/file/123174/eeg-txt.html

Thank you in advance.

Code for the above plot:

x = np.array([])
input = open('eeg.txt', 'r')
for file in input:
    file = file.replace(',','')
    x = np.append(x, float(file))
input.close()
plt.subplot(1, 1, 1)
plt.plot(x)
plt.ylabel('EEG signal')
plt.show()

FFT calculation:

import numpy as np
x = np.array([])
input = open('eeg.txt', 'r')
for file in input:
    file = file.replace(',','')
    x = np.append(x, float(file))
input.close()
plt.subplot(1, 1, 1)
ff = fft(x)
plt.plot(ff)
plt.ylabel('EEG signal')
plt.show()

Wavelet decomposition:

coeffs = wavedec(x, 'db4', level=6)
cA2, cD1, cD2,cD3,cD4,cD5,cD6 = coeffs

plt.subplot(7, 1, 1)
plt.plot(x)
plt.ylabel('Noisy Signal')
plt.subplot(7, 1, 2)
plt.plot(cD6)
plt.ylabel('noisy')
plt.subplot(7,1,3)
plt.plot(cD5)
plt.ylabel("gamma")
plt.subplot(7,1,4)
plt.plot(cD4)
plt.ylabel("beta")
plt.subplot(7,1,5)
plt.plot(cD3)
plt.ylabel("alpha")
plt.subplot(7,1,6)
plt.plot(cD2)
plt.ylabel("theta")
plt.subplot(7,1,7)
plt.plot(cD1)
plt.ylabel("delta")
plt.draw()
plt.show()

Results of wavelet:

Answer 1

What does it mean by sampling in EEG data?

Think of it this way. Some true EEG signal exists, but when you 'sample' you are grabbing little snippets of that signal to try and reconstruct it the way it really is. That signal has a frequency spectrum that looks like this

You must sample at a rate called "nyquist" to properly reconstruct the signal. That means at twice the highest frequency in that signal.

Also note that spike at 60 Hz. That probably isn't from the EEG but rather your power lines. Where are you located? 60 hz noise is very common in eeg/ekg signals. filter that out.

I am getting the sample rate and the frequency when I plot the data as shown below. Shouldn't it be the time and frequency?

Generally the signal frequency is plotted against the amplitude or power of the signal if you are analyzing the frequency spectrum (as shown). On the other hand, you might want to see the signal in the "time domain". What you probably have is the "sample number" without any reference to time, but if you know the sampling rate then you can convert the x-axis to time.

samples = 1:4097;    % 4097 samples
Fs = 200;            % Sampling Frequency (Hz)
t = samples/Fs;      % Time Vector (seconds)

Answer 2

It is hard to answer your question, since you do not seem to have experience with EEG data and/or general signal processing.

You say, your data is sampled at 200 Hz, which seems good to me for EEG data.

1. What does it mean by sampling in EEG data? That means, that the (continous) EEG signal is choped up into discrete values. This is always necessary for further signal processing with computers.

2. I am getting the sample rate and the frequency when I plot the data as shown below. Shouldn't it be the time and frequency?

I don't know what you mean by I am getting the sample rate and the frequency when I plot the data. You certainly don't. The sampling rate/frequency is a fixed number given by your experimental hardware. You don't get it from your data - you have to know it from your experiment to get meaningful results from your data.

I also don't know what Shouldn't it be the time and frequency? means. Your EEG data is certainly a voltage signal over time, hence you have a signal in time domain.

Your sampling rate is given from your experimental settings and is 200 Hz as you say. Hence, each time point is separated by $$\Delta t = \frac{1}{f} = \frac{1}{200\,\textrm{Hz}} = 5\,\textrm{ms}$$

Your total signal that you have plotted is therefore $$4097 \times 5\times 10^{-3}\textrm{s} = 20.485\,\textrm{s}$$ long.

That is what you know from your data. Any further data extraction is up to you or your research question. If you'd like to get the frequencies that are in the signal, try to Fourier-transform it and extract the frequency region that you are interested in. As I see it, you have some apparent frequency components at approx. 13.4 Hz, 57.7 Hz, 81.0 Hz, and 88.0 Hz. Probably you are only interested in the lower spectrum around 13.4 Hz...

Answer 3

Ok, a lot of you do not understand the question probably because it wasn't asked well. here is your solution:

When you plot your EEG data you get your amplitude on the y axis (which is what you are referring to as frequencies) and the data points of the sample on the x axis (which is what you meant by sample rate).

To get time on the x axis instead, this is what you need to do in python. recall your frequency = 200 Hz meaning your change in time is $= 1/200 = 0.005$ seconds

in python create an np array for your x axis like this:

x_axis = []
samples = 4097
start = 0

for n in range(samples):
    X_axis.append(start)
    start = start + 0.005
x_axis = np.array(x_axis)

Now plot this against your EEG data (y_axis) to get the required waveform you need.